Plotting lines and the group aesthetic in ggplot2

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In the words of Hadley himself:

The important thing [for a line graph with a factor on the horizontal axis] is to manually specify the grouping. By
default ggplot2 uses the combination of all categorical variables in
the plot to group geoms – that doesn’t work for this plot because you
get an individual line for each point. Manually specify group = 1
indicates you want a single line connecting all the points.

You can actually group the points in very different ways as demonstrated by koshke here

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